On the group of homeomorphisms on R: A revisit
Submitted: 2021-08-29
|Accepted: 2022-03-14
|Published: 2022-10-03
Copyright (c) 2022 Applied General Topology

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Keywords:
Group of homeomorphisms, Normal subgroups, Dynamical systems, Fixed points, Conjugacy, bounded functions
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Abstract:
In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R ([2], [6], [7] and [8]), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.
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